We perform scanning-gate microscopy on a quantum-point contact. It is defined in a high-mobility two-dimensional electron gas of an AlGaAs/GaAs heterostructure, giving rise to a weak disorder potential. The lever arm of the scanning tip is significan
tly smaller than that of the split gates defining the conducting channel of the quantum-point contact. We are able to observe that the conducting channel is shifted in real space when asymmetric gate voltages are applied. The observed shifts are consistent with transport data and numerical estimations.
Probing techniques with spatial resolution have the potential to lead to a better understanding of the microscopic physical processes and to novel routes for manipulating nanostructures. We present scanning-gate images of a graphene quantum dot which
is coupled to source and drain via two constrictions. We image and locate conductance resonances of the quantum dot in the Coulomb-blockade regime as well as resonances of localized states in the constrictions in real space.
We demonstrate that excited states in single-layer graphene quantum dots can be detected via direct transport experiments. Coulomb diamond measurements show distinct features of sequential tunneling through an excited state. Moreover, the onset of in
elastic cotunneling in the diamond region could be detected. For low magnetic fields, the positions of the single-particle energy levels fluctuate on the scale of a flux quantum penetrating the dot area. For higher magnetic fields, the transition to the formation of Landau levels is observed. Estimates based on the linear energy-momentum relation of graphene give carrier numbers of the order of 10 for our device.
We analytically calculate the energy spectrum of a circular graphene quantum dot with radius R subjected to a perpendicular magnetic field B by applying the infinite-mass boundary condition. We can retrieve well-known limits for the cases R, B going
to infinity and B going to zero. Our model is capable of capturing the essential details of recent experiments. Quantitative agreement between theory and experiment is limited due to the fact that a circular dot is not close enough to the experimental geometry, that disorder plays a significant role, and that interaction effects may be relevant.
